Divisibility Rule for 150: A Comprehensive Guide

In number theory, the divisibility rule for 150 is crucial for identifying whether a given number is divisible by 150. Understanding this rule helps simplify large number operations and validates the divisibility of 150 more efficiently. The rule combines the divisibility criteria for 3 and 50, as 150 is the product of these two numbers.

The Divisibility Rule of 150

To determine if a number is divisible by 150, it must meet two criteria:

1. Divisibility by 3

A number is divisible by 3 if the sum of its digits is divisible by 3. This rule is a fundamental concept in number theory, providing a simple method to check for divisibility without performing the actual division.

2. Divisibility by 50

A number is divisible by 50 if it ends in either 00 or 50. This rule is straightforward and easily recognizable, making it a handy tool for quick checks.

Combining the Rules: The Additional Rule for 150

By combining the divisibility rules for 3 and 50, a number is divisible by 150 if:

The sum of its digits is divisible by 3. The number ends in 00 or 50.

This comprehensive approach ensures accuracy and efficiency in determining the divisibility of 150.

Example: Checking Number Divisibility by 150

Let's test the number 600 to see if it is divisible by 150:

Sum of digits: 6 0 0 6, which is divisible by 3. The number ends in 00.

Since both conditions are met, 600 is divisible by 150. Indeed, 600 ÷ 150 4.

Let's try another example: 8234674050.

Divisibility by 50: Ignore the trailing 0's, and focus on the digits before them: 82346745. Sum the digits: 8 2 3 4 6 7 4 5 39. 39 ÷ 3 13, with no remainder.

Since the sum of the digits is divisible by 3, 8234674050 is divisible by 150. Checking with a calculator confirms that 8234674050 ÷ 150 54897827.

Conclusion

The divisibility rule for 150 is a powerful tool in number theory. By understanding and applying these rules, you can quickly and accurately determine whether a number is divisible by 150. This knowledge is invaluable for a wide range of mathematical and practical applications.